The Mathematics Of Chip Firing

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The Mathematics of Chip-Firing

Caroline J. Klivans
The Mathematics of Chip Firing Book PDF

Author : Caroline J. Klivans
Publisher : CRC Press
Page : 296 pages
File Size : 53,6 Mb
Release : 2018-11-15
Category : Computers
ISBN : 9781351800990

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The Mathematics of Chip-Firing by Caroline J. Klivans Pdf

The Mathematics of Chip-firing is a solid introduction and overview of the growing field of chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing refers to a discrete dynamical system — a commodity is exchanged between sites of a network according to very simple local rules. Although governed by local rules, the long-term global behavior of the system reveals fascinating properties. The Fundamental properties of chip-firing are covered from a variety of perspectives. This gives the reader both a broad context of the field and concrete entry points from different backgrounds. Broken into two sections, the first examines the fundamentals of chip-firing, while the second half presents more general frameworks for chip-firing. Instructors and students will discover that this book provides a comprehensive background to approaching original sources. Features: Provides a broad introduction for researchers interested in the subject of chip-firing The text includes historical and current perspectives Exercises included at the end of each chapter About the Author: Caroline J. Klivans received a BA degree in mathematics from Cornell University and a PhD in applied mathematics from MIT. Currently, she is an Associate Professor in the Division of Applied Mathematics at Brown University. She is also an Associate Director of ICERM (Institute for Computational and Experimental Research in Mathematics). Before coming to Brown she held positions at MSRI, Cornell and the University of Chicago. Her research is in algebraic, geometric and topological combinatorics.

Divisors and Sandpiles: An Introduction to Chip-Firing

Scott Corry,David Perkinson
Divisors and Sandpiles An Introduction to Chip Firing Book PDF

Author : Scott Corry,David Perkinson
Publisher : American Mathematical Soc.
Page : 325 pages
File Size : 46,6 Mb
Release : 2018-07-23
Category : Abelian groups
ISBN : 9781470442187

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Divisors and Sandpiles: An Introduction to Chip-Firing by Scott Corry,David Perkinson Pdf

Divisors and Sandpiles provides an introduction to the combinatorial theory of chip-firing on finite graphs. Part 1 motivates the study of the discrete Laplacian by introducing the dollar game. The resulting theory of divisors on graphs runs in close parallel to the geometric theory of divisors on Riemann surfaces, and Part 1 culminates in a full exposition of the graph-theoretic Riemann-Roch theorem due to M. Baker and S. Norine. The text leverages the reader's understanding of the discrete story to provide a brief overview of the classical theory of Riemann surfaces. Part 2 focuses on sandpiles, which are toy models of physical systems with dynamics controlled by the discrete Laplacian of the underlying graph. The text provides a careful introduction to the sandpile group and the abelian sandpile model, leading ultimately to L. Levine's threshold density theorem for the fixed-energy sandpile Markov chain. In a precise sense, the theory of sandpiles is dual to the theory of divisors, and there are many beautiful connections between the first two parts of the book. Part 3 addresses various topics connecting the theory of chip-firing to other areas of mathematics, including the matrix-tree theorem, harmonic morphisms, parking functions, M-matrices, matroids, the Tutte polynomial, and simplicial homology. The text is suitable for advanced undergraduates and beginning graduate students.

In and Out of Equilibrium 2

Vladas Sidoravicius,Maria Eulália Vares
In and Out of Equilibrium 2 Book PDF

Author : Vladas Sidoravicius,Maria Eulália Vares
Publisher : Springer Science & Business Media
Page : 570 pages
File Size : 51,7 Mb
Release : 2008-11-26
Category : Mathematics
ISBN : 9783764387860

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In and Out of Equilibrium 2 by Vladas Sidoravicius,Maria Eulália Vares Pdf

This volume consists of a collection of invited articles, written by some of the most distinguished probabilists, most of whom have been personally responsible for advances in the various subfields of probability.

Divisors and Sandpiles

Scott Corry,David Perkinson
Divisors and Sandpiles Book PDF

Author : Scott Corry,David Perkinson
Publisher : Unknown
Page : 128 pages
File Size : 41,6 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 1470448610

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Divisors and Sandpiles by Scott Corry,David Perkinson Pdf

Divisors and Sandpiles provides an introduction to the combinatorial theory of chip-firing on finite graphs. Part 1 motivates the study of the discrete Laplacian by introducing the dollar game. The resulting theory of divisors on graphs runs in close parallel to the geometric theory of divisors on Riemann surfaces, and Part 1 culminates in a full exposition of the graph-theoretic Riemann-Roch theorem due to M. Baker and S. Norine. The text leverages the reader's understanding of the discrete story to provide a brief overview of the classical theory of Riemann surfaces. Part 2 focuses on sandpi.

Adventures in Graph Theory

W. David Joyner,Caroline Grant Melles
Adventures in Graph Theory Book PDF

Author : W. David Joyner,Caroline Grant Melles
Publisher : Birkhäuser
Page : 327 pages
File Size : 46,6 Mb
Release : 2017-12-28
Category : Mathematics
ISBN : 9783319683836

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Adventures in Graph Theory by W. David Joyner,Caroline Grant Melles Pdf

This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. This book can also serve as a reference for anyone interested in exploring how they can apply graph theory to other parts of mathematics.

A Project-Based Guide to Undergraduate Research in Mathematics

Pamela E. Harris,Erik Insko,Aaron Wootton
A Project Based Guide to Undergraduate Research in Mathematics Book PDF

Author : Pamela E. Harris,Erik Insko,Aaron Wootton
Publisher : Springer Nature
Page : 324 pages
File Size : 53,9 Mb
Release : 2020-04-17
Category : Mathematics
ISBN : 9783030378530

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A Project-Based Guide to Undergraduate Research in Mathematics by Pamela E. Harris,Erik Insko,Aaron Wootton Pdf

This volume provides accessible and self-contained research problems designed for undergraduate student projects, and simultaneously promotes the development of sustainable undergraduate research programs. The chapters in this work span a variety of topical areas of pure and applied mathematics and mathematics education. Each chapter gives a self-contained introduction on a research topic with an emphasis on the specific tools and knowledge needed to create and maintain fruitful research programs for undergraduates. Some of the topics discussed include:• Disease modeling• Tropical curves and surfaces• Numerical semigroups• Mathematics EducationThis volume will primarily appeal to undergraduate students interested in pursuing research projects and faculty members seeking to mentor them. It may also aid students and faculty participating in independent studies and capstone projects.

Extended Abstracts EuroComb 2021

Jaroslav Nešetřil,Guillem Perarnau,Juanjo Rué,Oriol Serra
Extended Abstracts EuroComb 2021 Book PDF

Author : Jaroslav Nešetřil,Guillem Perarnau,Juanjo Rué,Oriol Serra
Publisher : Springer Nature
Page : 875 pages
File Size : 47,9 Mb
Release : 2021-08-23
Category : Mathematics
ISBN : 9783030838232

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Extended Abstracts EuroComb 2021 by Jaroslav Nešetřil,Guillem Perarnau,Juanjo Rué,Oriol Serra Pdf

This book collects the extended abstracts of the accepted contributions to EuroComb21. A similar book is published at every edition of EuroComb (every two years since 2001) collecting the most recent advances in combinatorics, graph theory, and related areas. It has a wide audience in the areas, and the papers are used and referenced broadly.

Illustrating Mathematics

Diana Davis
Illustrating Mathematics Book PDF

Author : Diana Davis
Publisher : American Mathematical Soc.
Page : 171 pages
File Size : 54,8 Mb
Release : 2020-10-16
Category : Education
ISBN : 9781470461225

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Illustrating Mathematics by Diana Davis Pdf

This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.

Handbook of Enumerative Combinatorics

Miklos Bona
Handbook of Enumerative Combinatorics Book PDF

Author : Miklos Bona
Publisher : CRC Press
Page : 1073 pages
File Size : 42,5 Mb
Release : 2015-03-24
Category : Mathematics
ISBN : 9781482220865

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Handbook of Enumerative Combinatorics by Miklos Bona Pdf

Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he

Game Theory, Alive

Anna R. Karlin,Yuval Peres
Game Theory Alive Book PDF

Author : Anna R. Karlin,Yuval Peres
Publisher : American Mathematical Soc.
Page : 372 pages
File Size : 51,5 Mb
Release : 2017-04-27
Category : Game theory
ISBN : 9781470419820

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Game Theory, Alive by Anna R. Karlin,Yuval Peres Pdf

We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities. This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. The importance of game-theoretic thinking transcends the academic setting—for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.

A Course in Combinatorics

J. H. van Lint,Richard Michael Wilson
A Course in Combinatorics Book PDF

Author : J. H. van Lint,Richard Michael Wilson
Publisher : Cambridge University Press
Page : 620 pages
File Size : 41,9 Mb
Release : 2001-11-22
Category : Mathematics
ISBN : 0521006015

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A Course in Combinatorics by J. H. van Lint,Richard Michael Wilson Pdf

This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.

Reflection Groups and Coxeter Groups

James E. Humphreys
Reflection Groups and Coxeter Groups Book PDF

Author : James E. Humphreys
Publisher : Cambridge University Press
Page : 222 pages
File Size : 50,9 Mb
Release : 1992-10
Category : Mathematics
ISBN : 0521436133

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Reflection Groups and Coxeter Groups by James E. Humphreys Pdf

This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.

Complexity: Knots, Colourings and Countings

D. J. A. Welsh
Complexity Knots Colourings and Countings Book PDF

Author : D. J. A. Welsh
Publisher : Cambridge University Press
Page : 176 pages
File Size : 53,5 Mb
Release : 1993-08-12
Category : Computers
ISBN : 0521457408

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Complexity: Knots, Colourings and Countings by D. J. A. Welsh Pdf

These notes are based on a series of lectures given at the Advanced Research Institute of Discrete Applied Mathematics, Rutgers University.

Mathematical Statistics with Applications in R

Kandethody M. Ramachandran,Chris P. Tsokos
Mathematical Statistics with Applications in R Book PDF

Author : Kandethody M. Ramachandran,Chris P. Tsokos
Publisher : Elsevier
Page : 825 pages
File Size : 41,8 Mb
Release : 2014-09-14
Category : Mathematics
ISBN : 9780124171329

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Mathematical Statistics with Applications in R by Kandethody M. Ramachandran,Chris P. Tsokos Pdf

Mathematical Statistics with Applications in R, Second Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining the discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem solving in a logical manner.This book provides a step-by-step procedure to solve real problems, making the topic more accessible. It includes goodness of fit methods to identify the probability distribution that characterizes the probabilistic behavior or a given set of data. Exercises as well as practical, real-world chapter projects are included, and each chapter has an optional section on using Minitab, SPSS and SAS commands. The text also boasts a wide array of coverage of ANOVA, nonparametric, MCMC, Bayesian and empirical methods; solutions to selected problems; data sets; and an image bank for students.Advanced undergraduate and graduate students taking a one or two semester mathematical statistics course will find this book extremely useful in their studies. Step-by-step procedure to solve real problems, making the topic more accessible Exercises blend theory and modern applications Practical, real-world chapter projects Provides an optional section in each chapter on using Minitab, SPSS and SAS commands Wide array of coverage of ANOVA, Nonparametric, MCMC, Bayesian and empirical methods

The Origin of Consciousness in the Breakdown of the Bicameral Mind

Julian Jaynes
The Origin of Consciousness in the Breakdown of the Bicameral Mind Book PDF

Author : Julian Jaynes
Publisher : Houghton Mifflin Harcourt
Page : 580 pages
File Size : 45,9 Mb
Release : 2000-08-15
Category : Psychology
ISBN : 9780547527543

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The Origin of Consciousness in the Breakdown of the Bicameral Mind by Julian Jaynes Pdf

National Book Award Finalist: “This man’s ideas may be the most influential, not to say controversial, of the second half of the twentieth century.”—Columbus Dispatch At the heart of this classic, seminal book is Julian Jaynes's still-controversial thesis that human consciousness did not begin far back in animal evolution but instead is a learned process that came about only three thousand years ago and is still developing. The implications of this revolutionary scientific paradigm extend into virtually every aspect of our psychology, our history and culture, our religion—and indeed our future. “Don’t be put off by the academic title of Julian Jaynes’s The Origin of Consciousness in the Breakdown of the Bicameral Mind. Its prose is always lucid and often lyrical…he unfolds his case with the utmost intellectual rigor.”—The New York Times “When Julian Jaynes . . . speculates that until late in the twentieth millennium BC men had no consciousness but were automatically obeying the voices of the gods, we are astounded but compelled to follow this remarkable thesis.”—John Updike, The New Yorker “He is as startling as Freud was in The Interpretation of Dreams, and Jaynes is equally as adept at forcing a new view of known human behavior.”—American Journal of Psychiatry